Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_black 2 1.706897
beta0_yellow 1 1.643353
beta1_black 7 1.638430
beta0_black 2 1.574073
beta3_pH 2 1.563121
beta1_pelagic 7 1.433399
beta0_pelagic 4 1.414224
beta2_pelagic 4 1.391266
beta2_yellow 3 1.363247
beta3_yellow 2 1.360292
parameter n badRhat_avg
beta0_pH 9 1.308021
beta1_pH 14 1.287420
beta2_black 3 1.266441
beta4_pelagic 4 1.208530
mu_beta0_pH 1 1.194019
beta2_pH 8 1.189640
beta3_pelagic 4 1.174974
beta1_yellow 4 1.138714
tau_beta0_yellow 1 1.135828
tau_beta0_pelagic 1 1.124783
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0
beta0_pelagic 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0
beta0_pH 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1
beta0_yellow 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta1_black 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0
beta1_pelagic 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1
beta1_pH 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1
beta1_yellow 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1
beta2_black 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0
beta2_pelagic 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1
beta2_pH 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0
beta2_yellow 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1
beta3_black 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0
beta3_pelagic 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1
beta3_pH 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0
beta3_yellow 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
beta4_pelagic 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.129 0.071 -0.260 -0.133 0.016
mu_bc_H[2] -0.094 0.046 -0.171 -0.100 0.009
mu_bc_H[3] -0.433 0.072 -0.568 -0.437 -0.282
mu_bc_H[4] -0.989 0.194 -1.386 -0.985 -0.625
mu_bc_H[5] 0.956 0.940 -0.154 0.759 3.482
mu_bc_H[6] -2.170 0.322 -2.801 -2.175 -1.529
mu_bc_H[7] -0.461 0.110 -0.683 -0.459 -0.250
mu_bc_H[8] 0.244 0.362 -0.353 0.205 1.085
mu_bc_H[9] -0.294 0.138 -0.561 -0.297 -0.017
mu_bc_H[10] -0.110 0.069 -0.241 -0.113 0.034
mu_bc_H[11] -0.124 0.037 -0.198 -0.125 -0.051
mu_bc_H[12] -0.254 0.105 -0.478 -0.248 -0.060
mu_bc_H[13] -0.135 0.078 -0.285 -0.138 0.026
mu_bc_H[14] -0.310 0.094 -0.503 -0.309 -0.133
mu_bc_H[15] -0.343 0.050 -0.439 -0.345 -0.240
mu_bc_H[16] -0.259 0.374 -0.901 -0.281 0.534
mu_bc_R[1] 1.294 0.143 1.010 1.289 1.576
mu_bc_R[2] 1.451 0.094 1.259 1.452 1.628
mu_bc_R[3] 1.387 0.142 1.094 1.387 1.659
mu_bc_R[4] 0.928 0.203 0.496 0.939 1.292
mu_bc_R[5] 1.110 0.481 0.159 1.118 2.017
mu_bc_R[6] -1.604 0.424 -2.445 -1.602 -0.776
mu_bc_R[7] 0.274 0.192 -0.095 0.272 0.648
mu_bc_R[8] 0.556 0.203 0.138 0.561 0.942
mu_bc_R[9] 0.348 0.206 -0.095 0.364 0.703
mu_bc_R[10] 1.333 0.128 1.068 1.338 1.571
mu_bc_R[11] 1.037 0.099 0.841 1.038 1.233
mu_bc_R[12] 0.822 0.205 0.421 0.825 1.218
mu_bc_R[13] 1.026 0.102 0.821 1.026 1.218
mu_bc_R[14] 0.897 0.142 0.604 0.905 1.182
mu_bc_R[15] 0.783 0.109 0.565 0.785 1.004
mu_bc_R[16] 1.095 0.128 0.841 1.097 1.347
tau_pH[1] 5.270 0.442 4.448 5.269 6.164
tau_pH[2] 2.372 0.319 1.795 2.347 3.047
tau_pH[3] 2.254 0.225 1.832 2.254 2.712
beta0_pH[1,1] 0.516 0.171 0.165 0.521 0.840
beta0_pH[2,1] 1.340 0.176 0.977 1.342 1.673
beta0_pH[3,1] 1.409 0.192 0.976 1.419 1.751
beta0_pH[4,1] 1.559 0.223 1.067 1.579 1.949
beta0_pH[5,1] -0.840 0.290 -1.466 -0.823 -0.315
beta0_pH[6,1] -0.677 0.448 -1.791 -0.592 -0.015
beta0_pH[7,1] 0.121 0.633 -1.049 0.146 0.925
beta0_pH[8,1] -0.664 0.269 -1.284 -0.634 -0.228
beta0_pH[9,1] -0.635 0.272 -1.218 -0.623 -0.136
beta0_pH[10,1] 0.184 0.194 -0.214 0.191 0.556
beta0_pH[11,1] -0.099 0.169 -0.459 -0.092 0.207
beta0_pH[12,1] 0.480 0.189 0.109 0.484 0.835
beta0_pH[13,1] -0.005 0.148 -0.312 -0.001 0.274
beta0_pH[14,1] -0.329 0.168 -0.669 -0.323 -0.009
beta0_pH[15,1] -0.051 0.178 -0.414 -0.046 0.283
beta0_pH[16,1] -0.530 0.419 -1.639 -0.433 0.041
beta0_pH[1,2] 2.722 0.219 2.198 2.745 3.083
beta0_pH[2,2] 2.796 0.227 2.134 2.830 3.125
beta0_pH[3,2] 2.678 0.405 1.929 2.653 3.333
beta0_pH[4,2] 2.705 0.322 1.946 2.795 3.142
beta0_pH[5,2] 4.527 1.531 2.452 4.210 8.304
beta0_pH[6,2] 2.834 0.307 2.255 2.842 3.379
beta0_pH[7,2] 1.882 0.378 1.344 1.926 2.266
beta0_pH[8,2] 2.810 0.253 2.375 2.835 3.157
beta0_pH[9,2] 2.748 0.781 1.458 2.815 3.756
beta0_pH[10,2] 3.666 0.324 3.113 3.692 4.084
beta0_pH[11,2] -4.858 0.293 -5.429 -4.856 -4.304
beta0_pH[12,2] -4.804 0.398 -5.616 -4.798 -4.056
beta0_pH[13,2] -4.578 0.390 -5.362 -4.580 -3.804
beta0_pH[14,2] -5.661 0.465 -6.605 -5.646 -4.790
beta0_pH[15,2] -4.233 0.326 -4.882 -4.233 -3.589
beta0_pH[16,2] -4.879 0.384 -5.695 -4.864 -4.153
beta0_pH[1,3] 0.542 0.607 -0.927 0.645 1.376
beta0_pH[2,3] 1.996 0.424 0.704 2.104 2.458
beta0_pH[3,3] 2.294 0.352 1.477 2.384 2.729
beta0_pH[4,3] 2.804 0.395 1.609 2.883 3.247
beta0_pH[5,3] 1.741 1.830 -1.174 1.517 6.334
beta0_pH[6,3] -0.445 0.994 -2.457 -0.538 1.467
beta0_pH[7,3] -1.957 0.757 -3.566 -1.908 -0.665
beta0_pH[8,3] 0.288 0.197 -0.101 0.288 0.664
beta0_pH[9,3] -0.728 0.628 -2.435 -0.572 0.084
beta0_pH[10,3] -0.011 1.009 -2.364 0.385 1.215
beta0_pH[11,3] -0.162 0.319 -0.739 -0.172 0.470
beta0_pH[12,3] -0.868 0.352 -1.623 -0.842 -0.259
beta0_pH[13,3] -0.137 0.305 -0.723 -0.138 0.469
beta0_pH[14,3] -0.279 0.258 -0.776 -0.278 0.245
beta0_pH[15,3] -0.722 0.287 -1.315 -0.707 -0.203
beta0_pH[16,3] -0.380 0.280 -0.913 -0.384 0.174
beta1_pH[1,1] 3.131 0.311 2.587 3.110 3.805
beta1_pH[2,1] 2.176 0.254 1.711 2.167 2.704
beta1_pH[3,1] 2.021 0.306 1.507 1.986 2.744
beta1_pH[4,1] 2.413 0.362 1.850 2.368 3.275
beta1_pH[5,1] 2.276 0.357 1.671 2.240 3.068
beta1_pH[6,1] 3.900 1.112 2.321 3.688 6.668
beta1_pH[7,1] 2.090 1.490 0.264 1.963 5.133
beta1_pH[8,1] 4.136 1.072 2.632 3.884 6.708
beta1_pH[9,1] 2.306 0.372 1.674 2.276 3.131
beta1_pH[10,1] 2.450 0.284 1.943 2.435 3.028
beta1_pH[11,1] 3.277 0.215 2.871 3.268 3.727
beta1_pH[12,1] 2.555 0.221 2.114 2.555 2.996
beta1_pH[13,1] 2.976 0.213 2.581 2.970 3.411
beta1_pH[14,1] 3.431 0.219 3.018 3.429 3.867
beta1_pH[15,1] 2.558 0.222 2.139 2.552 2.995
beta1_pH[16,1] 4.105 0.640 3.195 3.981 5.671
beta1_pH[1,2] 1.064 2.720 0.000 0.195 8.499
beta1_pH[2,2] 1.404 3.975 0.000 0.158 13.467
beta1_pH[3,2] 0.816 1.359 0.000 0.920 1.760
beta1_pH[4,2] 1.365 5.074 0.000 0.515 11.744
beta1_pH[5,2] 9.097 31.089 0.000 1.198 81.804
beta1_pH[6,2] 1.403 2.529 0.000 1.203 3.791
beta1_pH[7,2] 1.636 3.098 0.000 0.553 11.378
beta1_pH[8,2] 27.050 62.468 0.000 0.763 219.862
beta1_pH[9,2] 3.196 15.466 0.000 1.174 15.798
beta1_pH[10,2] 13.684 27.396 0.000 2.856 101.012
beta1_pH[11,2] 6.699 0.319 6.084 6.687 7.344
beta1_pH[12,2] 6.496 0.476 5.634 6.476 7.543
beta1_pH[13,2] 6.988 0.428 6.171 6.981 7.862
beta1_pH[14,2] 7.310 0.488 6.410 7.299 8.301
beta1_pH[15,2] 6.729 0.350 6.044 6.727 7.425
beta1_pH[16,2] 7.488 0.418 6.703 7.476 8.348
beta1_pH[1,3] 3.094 1.259 1.608 2.763 6.479
beta1_pH[2,3] 0.937 2.149 0.000 0.219 7.844
beta1_pH[3,3] 0.551 1.199 0.000 0.145 3.473
beta1_pH[4,3] 8.082 24.264 0.000 0.158 90.425
beta1_pH[5,3] 2.671 1.928 0.770 2.531 6.607
beta1_pH[6,3] 2.340 1.065 0.834 2.332 4.398
beta1_pH[7,3] 2.815 0.764 1.511 2.748 4.463
beta1_pH[8,3] 2.758 0.378 2.063 2.743 3.480
beta1_pH[9,3] 2.794 0.654 1.870 2.672 4.616
beta1_pH[10,3] 3.406 1.089 2.036 3.016 6.036
beta1_pH[11,3] 2.750 0.382 2.004 2.750 3.506
beta1_pH[12,3] 4.125 0.437 3.351 4.095 5.058
beta1_pH[13,3] 1.720 0.329 1.083 1.723 2.344
beta1_pH[14,3] 2.518 0.332 1.868 2.516 3.161
beta1_pH[15,3] 2.012 0.310 1.440 2.001 2.614
beta1_pH[16,3] 1.779 0.312 1.141 1.783 2.388
beta2_pH[1,1] 0.466 0.116 0.283 0.453 0.727
beta2_pH[2,1] 0.564 0.301 0.261 0.506 1.202
beta2_pH[3,1] 0.613 0.392 0.229 0.531 1.602
beta2_pH[4,1] 0.467 0.190 0.200 0.438 0.891
beta2_pH[5,1] 1.390 1.161 0.246 1.099 4.458
beta2_pH[6,1] 0.185 0.066 0.092 0.174 0.347
beta2_pH[7,1] -0.248 1.542 -4.917 0.032 1.915
beta2_pH[8,1] 0.239 0.084 0.125 0.227 0.447
beta2_pH[9,1] 0.444 0.228 0.181 0.402 0.951
beta2_pH[10,1] 0.607 0.328 0.291 0.544 1.240
beta2_pH[11,1] 0.780 0.210 0.472 0.752 1.279
beta2_pH[12,1] 1.344 0.459 0.744 1.244 2.568
beta2_pH[13,1] 0.734 0.212 0.420 0.708 1.234
beta2_pH[14,1] 0.833 0.234 0.528 0.801 1.316
beta2_pH[15,1] 0.797 0.290 0.414 0.745 1.462
beta2_pH[16,1] 0.384 0.168 0.177 0.339 0.814
beta2_pH[1,2] -3.599 8.991 -21.107 -3.558 14.935
beta2_pH[2,2] -4.110 8.884 -21.484 -4.201 15.879
beta2_pH[3,2] -4.745 8.481 -21.514 -4.619 15.222
beta2_pH[4,2] -4.654 8.601 -21.349 -4.541 15.430
beta2_pH[5,2] -8.108 8.198 -24.522 -7.864 9.634
beta2_pH[6,2] -8.375 7.957 -24.700 -7.862 10.919
beta2_pH[7,2] -8.391 7.845 -24.027 -8.087 9.021
beta2_pH[8,2] -8.330 8.045 -24.336 -7.880 9.765
beta2_pH[9,2] -8.413 7.933 -24.295 -8.093 9.528
beta2_pH[10,2] -8.689 7.847 -24.493 -8.244 10.103
beta2_pH[11,2] -8.793 3.759 -18.214 -7.929 -3.927
beta2_pH[12,2] -6.174 4.396 -16.862 -5.350 -0.803
beta2_pH[13,2] -6.196 4.198 -16.977 -5.070 -1.515
beta2_pH[14,2] -7.275 3.925 -16.606 -6.310 -2.291
beta2_pH[15,2] -8.622 3.707 -17.488 -7.869 -3.608
beta2_pH[16,2] -8.777 3.723 -18.023 -8.016 -3.808
beta2_pH[1,3] 2.529 4.283 0.127 0.501 15.505
beta2_pH[2,3] 1.046 6.046 -10.488 0.603 16.294
beta2_pH[3,3] 0.700 5.968 -9.637 -0.147 15.538
beta2_pH[4,3] 0.859 5.881 -9.591 0.113 15.298
beta2_pH[5,3] 7.426 6.118 0.069 6.286 23.240
beta2_pH[6,3] 7.520 6.133 0.154 6.342 22.945
beta2_pH[7,3] 7.127 6.070 0.525 5.593 22.251
beta2_pH[8,3] 8.607 5.675 1.095 7.472 22.856
beta2_pH[9,3] 7.076 6.127 0.332 5.714 22.077
beta2_pH[10,3] 6.179 6.538 0.313 4.047 22.262
beta2_pH[11,3] -2.288 2.188 -8.809 -1.667 -0.634
beta2_pH[12,3] -2.376 1.870 -7.996 -1.836 -0.933
beta2_pH[13,3] -2.891 2.310 -9.251 -2.152 -0.812
beta2_pH[14,3] -2.869 2.373 -10.058 -2.120 -0.918
beta2_pH[15,3] -3.005 2.346 -9.797 -2.250 -0.984
beta2_pH[16,3] -3.066 2.453 -9.999 -2.267 -0.909
beta3_pH[1,1] 35.855 0.803 34.342 35.837 37.529
beta3_pH[2,1] 33.413 1.110 31.442 33.321 35.737
beta3_pH[3,1] 33.754 1.054 31.597 33.727 35.905
beta3_pH[4,1] 33.854 1.195 31.741 33.767 36.493
beta3_pH[5,1] 27.856 1.221 26.455 27.550 31.192
beta3_pH[6,1] 38.802 3.166 32.948 38.615 45.208
beta3_pH[7,1] 30.829 9.646 18.379 29.241 45.742
beta3_pH[8,1] 40.247 2.262 36.405 39.963 45.253
beta3_pH[9,1] 30.670 1.501 28.156 30.562 33.764
beta3_pH[10,1] 32.586 0.869 31.050 32.545 34.403
beta3_pH[11,1] 30.297 0.466 29.404 30.290 31.215
beta3_pH[12,1] 30.149 0.394 29.355 30.161 30.882
beta3_pH[13,1] 33.136 0.586 32.045 33.117 34.372
beta3_pH[14,1] 32.015 0.460 31.138 32.007 32.931
beta3_pH[15,1] 31.149 0.651 29.841 31.140 32.453
beta3_pH[16,1] 31.689 1.028 29.225 31.733 33.714
beta3_pH[1,2] 29.877 8.399 18.441 28.139 44.593
beta3_pH[2,2] 27.159 7.707 18.279 24.303 44.308
beta3_pH[3,2] 37.428 7.616 19.144 41.387 44.331
beta3_pH[4,2] 32.342 8.395 18.749 31.369 44.538
beta3_pH[5,2] 30.945 8.081 18.448 30.787 45.106
beta3_pH[6,2] 33.834 5.311 19.640 35.288 43.939
beta3_pH[7,2] 28.104 7.507 18.347 26.235 44.582
beta3_pH[8,2] 27.000 6.828 18.348 25.336 43.201
beta3_pH[9,2] 37.724 9.262 18.812 43.540 45.713
beta3_pH[10,2] 29.645 5.109 19.078 29.940 41.658
beta3_pH[11,2] 43.396 0.170 43.125 43.371 43.753
beta3_pH[12,2] 43.185 0.189 42.829 43.158 43.636
beta3_pH[13,2] 43.850 0.145 43.489 43.888 44.036
beta3_pH[14,2] 43.297 0.185 43.056 43.256 43.766
beta3_pH[15,2] 43.397 0.182 43.115 43.375 43.789
beta3_pH[16,2] 43.498 0.179 43.171 43.493 43.835
beta3_pH[1,3] 38.881 2.289 34.109 39.394 43.566
beta3_pH[2,3] 29.624 7.696 18.423 29.151 44.680
beta3_pH[3,3] 31.578 8.641 18.411 31.458 44.427
beta3_pH[4,3] 27.934 7.631 18.309 25.836 44.532
beta3_pH[5,3] 27.562 6.940 18.331 26.198 43.083
beta3_pH[6,3] 27.627 6.316 18.798 25.816 43.864
beta3_pH[7,3] 26.577 1.222 24.767 26.406 29.052
beta3_pH[8,3] 41.494 0.306 40.999 41.490 41.997
beta3_pH[9,3] 32.951 1.531 28.331 33.450 34.320
beta3_pH[10,3] 35.035 1.546 31.510 35.798 36.840
beta3_pH[11,3] 41.771 0.779 40.168 41.805 43.223
beta3_pH[12,3] 41.731 0.391 40.993 41.746 42.505
beta3_pH[13,3] 42.762 0.856 41.107 42.783 44.694
beta3_pH[14,3] 41.111 0.554 39.901 41.134 42.114
beta3_pH[15,3] 42.632 0.653 41.173 42.699 43.721
beta3_pH[16,3] 42.878 0.745 41.141 42.999 44.085
beta0_pelagic[1] 1.933 0.436 0.806 2.087 2.404
beta0_pelagic[2] 1.342 0.301 0.489 1.424 1.714
beta0_pelagic[3] 0.235 0.323 -0.594 0.274 0.761
beta0_pelagic[4] 0.062 0.658 -1.758 0.222 0.993
beta0_pelagic[5] -0.157 1.584 -3.359 0.848 1.451
beta0_pelagic[6] 1.091 0.609 -0.449 1.308 1.686
beta0_pelagic[7] 1.569 0.150 1.287 1.574 1.854
beta0_pelagic[8] 1.688 0.215 1.284 1.709 1.977
beta0_pelagic[9] 2.048 0.814 0.038 2.278 2.907
beta0_pelagic[10] 2.478 0.295 1.545 2.528 2.787
beta0_pelagic[11] 0.012 0.485 -1.001 0.037 0.715
beta0_pelagic[12] 1.686 0.137 1.422 1.686 1.952
beta0_pelagic[13] 0.314 0.193 -0.105 0.324 0.664
beta0_pelagic[14] -0.145 0.305 -0.854 -0.104 0.322
beta0_pelagic[15] -0.261 0.128 -0.507 -0.260 -0.013
beta0_pelagic[16] 0.257 0.341 -0.682 0.351 0.663
beta1_pelagic[1] 0.327 0.449 0.000 0.106 1.506
beta1_pelagic[2] 0.235 0.313 0.000 0.084 1.095
beta1_pelagic[3] 0.846 0.449 0.024 0.778 2.117
beta1_pelagic[4] 1.117 0.689 0.004 0.950 2.984
beta1_pelagic[5] 1.432 1.703 0.000 0.173 4.854
beta1_pelagic[6] 0.542 0.853 0.000 0.104 2.697
beta1_pelagic[7] 7.862 11.904 0.000 0.101 37.133
beta1_pelagic[8] 0.285 0.948 0.000 0.005 2.988
beta1_pelagic[9] 0.845 0.964 0.000 0.691 3.318
beta1_pelagic[10] 0.294 1.175 0.000 0.007 2.476
beta1_pelagic[11] 3.872 1.220 2.146 3.799 6.418
beta1_pelagic[12] 2.781 0.287 2.232 2.778 3.362
beta1_pelagic[13] 2.884 0.738 1.772 2.784 4.605
beta1_pelagic[14] 4.526 1.085 2.878 4.342 6.980
beta1_pelagic[15] 2.910 0.243 2.427 2.912 3.383
beta1_pelagic[16] 3.736 1.140 2.695 3.308 7.087
beta2_pelagic[1] 1.770 2.765 -3.843 1.370 8.218
beta2_pelagic[2] 1.901 2.473 -2.218 1.404 7.988
beta2_pelagic[3] 1.970 2.115 0.096 1.259 7.300
beta2_pelagic[4] 2.214 2.285 0.144 1.466 8.145
beta2_pelagic[5] -1.179 3.998 -8.603 -1.954 7.516
beta2_pelagic[6] 1.218 3.879 -7.038 1.160 8.829
beta2_pelagic[7] -1.358 4.255 -9.307 -1.830 7.708
beta2_pelagic[8] -0.284 4.243 -8.522 -0.369 8.237
beta2_pelagic[9] 1.285 3.562 -6.608 1.022 8.604
beta2_pelagic[10] 0.087 4.234 -8.362 0.204 8.481
beta2_pelagic[11] 1.251 2.117 0.111 0.235 7.567
beta2_pelagic[12] 4.655 2.351 1.463 4.152 10.461
beta2_pelagic[13] 0.761 0.962 0.197 0.471 3.346
beta2_pelagic[14] 0.296 0.118 0.144 0.271 0.561
beta2_pelagic[15] 4.931 2.354 1.624 4.471 10.701
beta2_pelagic[16] 3.242 2.817 0.164 2.880 9.842
beta3_pelagic[1] 27.331 7.737 18.334 24.351 44.902
beta3_pelagic[2] 29.110 8.423 18.446 26.983 45.319
beta3_pelagic[3] 30.055 4.292 22.724 29.937 41.398
beta3_pelagic[4] 25.165 3.262 19.677 25.173 33.529
beta3_pelagic[5] 36.373 10.053 18.934 40.007 45.995
beta3_pelagic[6] 30.246 6.882 18.667 29.822 44.272
beta3_pelagic[7] 25.678 7.868 18.268 21.388 43.974
beta3_pelagic[8] 28.972 8.060 18.379 27.193 44.573
beta3_pelagic[9] 29.300 6.510 18.953 27.655 43.763
beta3_pelagic[10] 28.610 8.096 18.248 27.115 44.287
beta3_pelagic[11] 42.540 1.871 37.826 43.031 45.268
beta3_pelagic[12] 43.447 0.240 43.018 43.434 43.906
beta3_pelagic[13] 42.682 1.350 40.221 42.545 45.550
beta3_pelagic[14] 42.522 1.682 39.202 42.497 45.678
beta3_pelagic[15] 43.177 0.216 42.685 43.185 43.582
beta3_pelagic[16] 43.197 0.777 41.450 43.228 45.332
mu_beta0_pelagic[1] 0.840 0.836 -0.928 0.848 2.591
mu_beta0_pelagic[2] 1.395 0.774 -0.460 1.547 2.570
mu_beta0_pelagic[3] 0.311 0.458 -0.629 0.325 1.188
tau_beta0_pelagic[1] 1.223 2.721 0.065 0.614 5.435
tau_beta0_pelagic[2] 1.762 3.597 0.074 0.814 8.418
tau_beta0_pelagic[3] 1.515 1.126 0.184 1.238 4.370
beta0_yellow[1] -0.547 0.207 -1.007 -0.526 -0.237
beta0_yellow[2] 0.472 0.193 0.073 0.490 0.773
beta0_yellow[3] -0.315 0.197 -0.768 -0.306 0.036
beta0_yellow[4] 0.737 0.367 -0.364 0.825 1.172
beta0_yellow[5] -1.200 0.403 -2.001 -1.191 -0.429
beta0_yellow[6] 0.280 0.211 -0.135 0.280 0.689
beta0_yellow[7] 0.435 0.913 -1.619 0.927 1.325
beta0_yellow[8] 0.630 0.678 -1.220 0.896 1.269
beta0_yellow[9] -0.141 0.304 -0.667 -0.133 0.385
beta0_yellow[10] 0.233 0.150 -0.051 0.232 0.532
beta0_yellow[11] -1.971 0.447 -2.894 -1.958 -1.082
beta0_yellow[12] -3.674 0.420 -4.550 -3.658 -2.903
beta0_yellow[13] -3.767 0.475 -4.759 -3.732 -2.943
beta0_yellow[14] -2.155 0.489 -3.069 -2.181 -1.140
beta0_yellow[15] -2.904 0.422 -3.794 -2.892 -2.091
beta0_yellow[16] -2.461 0.457 -3.392 -2.457 -1.622
beta1_yellow[1] 0.476 0.613 0.000 0.289 1.812
beta1_yellow[2] 1.145 0.507 0.598 1.047 2.598
beta1_yellow[3] 0.675 0.306 0.064 0.660 1.371
beta1_yellow[4] 1.669 0.988 0.708 1.327 4.522
beta1_yellow[5] 3.098 2.672 1.339 2.757 6.396
beta1_yellow[6] 2.247 0.346 1.584 2.244 2.926
beta1_yellow[7] 5.701 8.814 0.291 2.648 34.225
beta1_yellow[8] 2.255 2.623 0.021 1.717 10.890
beta1_yellow[9] 1.611 0.482 0.861 1.590 2.484
beta1_yellow[10] 2.317 0.460 1.534 2.281 3.269
beta1_yellow[11] 2.113 0.441 1.227 2.112 2.983
beta1_yellow[12] 2.483 0.425 1.703 2.467 3.370
beta1_yellow[13] 2.885 0.476 2.095 2.847 3.911
beta1_yellow[14] 2.224 0.486 1.216 2.240 3.161
beta1_yellow[15] 2.144 0.419 1.350 2.128 3.009
beta1_yellow[16] 2.211 0.452 1.352 2.201 3.131
beta2_yellow[1] -1.986 2.641 -8.432 -1.457 2.576
beta2_yellow[2] -2.118 2.076 -8.153 -1.516 -0.134
beta2_yellow[3] -2.351 2.290 -8.329 -1.597 -0.118
beta2_yellow[4] -1.517 1.960 -7.160 -0.720 -0.072
beta2_yellow[5] -4.086 2.741 -10.582 -3.561 -0.461
beta2_yellow[6] 3.706 2.312 0.957 3.124 9.698
beta2_yellow[7] -1.862 4.698 -10.677 -2.346 7.273
beta2_yellow[8] -1.632 3.582 -9.299 -1.325 6.001
beta2_yellow[9] 3.966 2.610 0.232 3.565 10.087
beta2_yellow[10] -4.322 2.625 -10.956 -3.817 -0.789
beta2_yellow[11] -4.050 2.245 -9.965 -3.526 -1.266
beta2_yellow[12] -4.228 2.195 -9.994 -3.752 -1.361
beta2_yellow[13] -4.176 2.136 -10.051 -3.656 -1.593
beta2_yellow[14] -4.217 2.291 -10.156 -3.842 -0.899
beta2_yellow[15] -3.776 2.259 -9.338 -3.321 -0.940
beta2_yellow[16] -4.332 2.118 -10.126 -3.988 -1.578
beta3_yellow[1] 27.708 7.831 18.280 25.073 44.572
beta3_yellow[2] 29.119 2.099 23.893 29.083 32.872
beta3_yellow[3] 33.058 3.430 24.473 32.958 41.213
beta3_yellow[4] 28.860 3.879 20.099 28.179 36.115
beta3_yellow[5] 33.332 1.645 30.097 33.388 36.268
beta3_yellow[6] 39.674 0.516 38.778 39.652 40.818
beta3_yellow[7] 22.510 4.281 18.555 20.418 33.648
beta3_yellow[8] 25.472 6.170 18.286 24.115 43.898
beta3_yellow[9] 37.662 1.953 36.006 37.584 42.466
beta3_yellow[10] 29.324 0.609 27.907 29.408 30.102
beta3_yellow[11] 45.334 0.508 44.115 45.428 45.974
beta3_yellow[12] 43.330 0.421 42.598 43.299 44.171
beta3_yellow[13] 44.859 0.370 44.028 44.919 45.468
beta3_yellow[14] 44.284 0.856 43.140 44.263 45.815
beta3_yellow[15] 45.052 1.607 44.095 45.183 45.971
beta3_yellow[16] 44.570 0.637 43.433 44.551 45.836
mu_beta0_yellow[1] 0.080 0.538 -1.013 0.083 1.223
mu_beta0_yellow[2] 0.032 0.497 -0.999 0.040 1.025
mu_beta0_yellow[3] -2.491 0.605 -3.447 -2.568 -0.990
tau_beta0_yellow[1] 2.164 3.281 0.109 1.280 9.582
tau_beta0_yellow[2] 1.525 2.115 0.143 1.051 5.424
tau_beta0_yellow[3] 1.401 1.570 0.113 0.914 5.712
beta0_black[1] 0.003 0.199 -0.360 -0.010 0.388
beta0_black[2] 1.893 0.139 1.621 1.897 2.135
beta0_black[3] 1.302 0.139 1.022 1.306 1.562
beta0_black[4] 1.983 0.438 0.738 2.035 2.556
beta0_black[5] 1.578 2.066 -3.110 1.665 5.669
beta0_black[6] 1.560 2.012 -2.946 1.653 5.399
beta0_black[7] 1.598 1.972 -2.775 1.673 5.648
beta0_black[8] 1.269 0.233 0.831 1.273 1.722
beta0_black[9] 2.416 0.278 1.850 2.428 2.924
beta0_black[10] 1.455 0.137 1.192 1.459 1.725
beta0_black[11] 3.463 0.166 3.137 3.470 3.765
beta0_black[12] 4.465 0.190 4.086 4.465 4.832
beta0_black[13] -0.005 0.336 -0.526 -0.055 0.887
beta0_black[14] 1.921 0.827 -0.359 2.166 2.823
beta0_black[15] 1.273 0.186 0.916 1.287 1.586
beta0_black[16] 4.229 0.254 3.721 4.253 4.560
beta2_black[1] 2.092 3.036 -4.496 2.058 8.660
beta2_black[2] -0.183 3.382 -7.385 -0.195 6.895
beta2_black[3] -0.042 3.275 -6.950 0.074 6.385
beta2_black[4] -1.467 2.496 -7.661 -1.084 3.471
beta2_black[5] -0.169 3.383 -7.187 -0.143 6.954
beta2_black[6] -0.037 3.253 -6.701 -0.096 6.892
beta2_black[7] -0.069 3.245 -6.847 -0.104 6.739
beta2_black[8] -0.196 3.333 -7.152 -0.261 6.653
beta2_black[9] -0.197 3.409 -7.270 -0.276 6.965
beta2_black[10] -0.248 3.360 -7.342 -0.301 6.836
beta2_black[11] -1.161 1.959 -5.461 -1.046 3.023
beta2_black[12] -2.280 1.580 -6.694 -1.881 -0.452
beta2_black[13] -1.955 1.544 -6.270 -1.503 -0.450
beta2_black[14] -1.088 1.486 -5.273 -0.554 -0.048
beta2_black[15] -1.106 2.223 -5.777 -1.132 4.061
beta2_black[16] -0.892 2.329 -5.630 -0.971 4.430
beta3_black[1] 37.868 7.127 19.412 41.414 43.639
beta3_black[2] 30.139 8.016 18.424 29.228 45.033
beta3_black[3] 30.200 7.997 18.454 29.493 44.835
beta3_black[4] 32.293 4.901 19.745 32.781 41.674
beta3_black[5] 30.026 7.952 18.470 29.166 44.867
beta3_black[6] 30.099 8.059 18.456 29.147 45.125
beta3_black[7] 29.939 7.930 18.404 29.154 44.816
beta3_black[8] 30.014 8.037 18.464 29.097 45.034
beta3_black[9] 30.334 8.055 18.370 29.776 45.077
beta3_black[10] 30.021 8.232 18.474 28.964 45.299
beta3_black[11] 31.468 7.684 18.732 31.458 44.796
beta3_black[12] 32.437 1.347 28.883 32.742 33.794
beta3_black[13] 39.041 1.940 36.647 39.315 40.651
beta3_black[14] 36.374 5.944 20.215 37.983 45.030
beta3_black[15] 31.654 7.932 18.730 31.783 45.179
beta3_black[16] 31.097 7.966 18.643 30.798 45.034
beta4_black[1] -0.261 0.187 -0.619 -0.260 0.104
beta4_black[2] 0.253 0.179 -0.099 0.253 0.611
beta4_black[3] -0.936 0.187 -1.307 -0.940 -0.559
beta4_black[4] 0.535 0.223 0.108 0.535 0.967
beta4_black[5] 0.238 2.553 -4.191 0.194 5.050
beta4_black[6] 0.221 2.373 -4.413 0.157 4.938
beta4_black[7] 0.193 2.435 -4.075 0.138 5.029
beta4_black[8] -0.697 0.366 -1.435 -0.694 0.007
beta4_black[9] 1.480 1.015 -0.105 1.349 3.800
beta4_black[10] 0.026 0.184 -0.337 0.024 0.384
beta4_black[11] -0.696 0.209 -1.112 -0.692 -0.290
beta4_black[12] 0.308 0.332 -0.311 0.300 0.999
beta4_black[13] -1.200 0.216 -1.625 -1.198 -0.792
beta4_black[14] -0.118 0.232 -0.570 -0.121 0.354
beta4_black[15] -0.894 0.211 -1.311 -0.895 -0.492
beta4_black[16] -0.595 0.224 -1.018 -0.594 -0.157
mu_beta0_black[1] 1.190 0.860 -0.755 1.225 2.872
mu_beta0_black[2] 1.598 0.917 -0.561 1.643 3.321
mu_beta0_black[3] 2.317 0.955 0.190 2.373 4.077
tau_beta0_black[1] 0.847 0.841 0.060 0.573 3.157
tau_beta0_black[2] 2.087 4.362 0.053 0.858 11.784
tau_beta0_black[3] 0.259 0.181 0.052 0.214 0.744
beta0_dsr[11] -2.905 0.274 -3.457 -2.901 -2.377
beta0_dsr[12] 4.527 0.316 3.998 4.528 5.068
beta0_dsr[13] -1.332 0.300 -1.916 -1.320 -0.772
beta0_dsr[14] -3.647 0.488 -4.663 -3.642 -2.713
beta0_dsr[15] -1.939 0.276 -2.479 -1.938 -1.401
beta0_dsr[16] -2.988 0.354 -3.686 -2.980 -2.314
beta1_dsr[11] 4.837 0.288 4.288 4.831 5.400
beta1_dsr[12] 6.510 8.807 2.219 4.976 20.118
beta1_dsr[13] 2.845 0.332 2.271 2.832 3.472
beta1_dsr[14] 6.314 0.524 5.329 6.317 7.409
beta1_dsr[15] 3.333 0.279 2.791 3.338 3.898
beta1_dsr[16] 5.812 0.369 5.108 5.808 6.554
beta2_dsr[11] -8.203 2.264 -13.646 -7.911 -4.689
beta2_dsr[12] -7.067 2.616 -12.919 -6.848 -2.364
beta2_dsr[13] -6.510 2.679 -12.151 -6.398 -1.619
beta2_dsr[14] -6.170 2.690 -11.770 -6.013 -1.794
beta2_dsr[15] -7.840 2.411 -13.254 -7.501 -4.037
beta2_dsr[16] -7.930 2.351 -13.472 -7.556 -4.325
beta3_dsr[11] 43.489 0.149 43.218 43.485 43.772
beta3_dsr[12] 33.990 0.710 32.305 34.130 34.811
beta3_dsr[13] 43.243 0.283 42.843 43.189 43.855
beta3_dsr[14] 43.334 0.223 43.075 43.266 43.917
beta3_dsr[15] 43.513 0.183 43.172 43.510 43.855
beta3_dsr[16] 43.438 0.156 43.175 43.427 43.762
beta4_dsr[11] 0.585 0.210 0.173 0.582 1.021
beta4_dsr[12] 0.249 0.447 -0.622 0.243 1.182
beta4_dsr[13] -0.174 0.211 -0.607 -0.171 0.233
beta4_dsr[14] 0.144 0.245 -0.337 0.145 0.619
beta4_dsr[15] 0.728 0.206 0.331 0.725 1.143
beta4_dsr[16] 0.130 0.225 -0.323 0.129 0.568
beta0_slope[11] -1.936 0.161 -2.255 -1.933 -1.619
beta0_slope[12] -4.658 0.266 -5.196 -4.653 -4.150
beta0_slope[13] -1.342 0.202 -1.773 -1.330 -1.005
beta0_slope[14] -2.635 0.176 -2.976 -2.635 -2.290
beta0_slope[15] -1.376 0.165 -1.704 -1.375 -1.056
beta0_slope[16] -2.728 0.170 -3.066 -2.726 -2.406
beta1_slope[11] 4.583 0.289 4.020 4.574 5.162
beta1_slope[12] 5.013 0.517 4.035 5.004 6.052
beta1_slope[13] 2.939 0.545 2.239 2.860 4.660
beta1_slope[14] 6.520 0.557 5.471 6.508 7.628
beta1_slope[15] 3.052 0.289 2.490 3.052 3.634
beta1_slope[16] 5.368 0.384 4.641 5.364 6.117
beta2_slope[11] 8.049 2.365 4.553 7.679 13.710
beta2_slope[12] 7.176 2.552 2.974 6.895 12.911
beta2_slope[13] 5.623 3.051 0.370 5.636 12.111
beta2_slope[14] 6.585 2.514 2.430 6.317 12.262
beta2_slope[15] 7.560 2.426 3.644 7.232 13.378
beta2_slope[16] 7.644 2.398 3.819 7.256 13.225
beta3_slope[11] 43.476 0.150 43.208 43.473 43.767
beta3_slope[12] 43.422 0.232 43.066 43.394 43.883
beta3_slope[13] 43.651 0.447 42.946 43.708 44.438
beta3_slope[14] 43.317 0.175 43.091 43.272 43.760
beta3_slope[15] 43.511 0.195 43.158 43.507 43.872
beta3_slope[16] 43.456 0.169 43.167 43.444 43.796
beta4_slope[11] -0.568 0.215 -0.981 -0.568 -0.158
beta4_slope[12] -1.434 0.664 -2.919 -1.353 -0.361
beta4_slope[13] 0.054 0.215 -0.353 0.054 0.467
beta4_slope[14] -0.190 0.256 -0.677 -0.195 0.321
beta4_slope[15] -0.722 0.211 -1.127 -0.721 -0.311
beta4_slope[16] -0.187 0.227 -0.611 -0.193 0.262
sigma_H[1] 0.200 0.054 0.104 0.196 0.311
sigma_H[2] 0.172 0.030 0.118 0.170 0.235
sigma_H[3] 0.195 0.043 0.120 0.191 0.285
sigma_H[4] 0.419 0.078 0.294 0.409 0.598
sigma_H[5] 0.989 0.212 0.599 0.975 1.434
sigma_H[6] 0.401 0.199 0.044 0.397 0.813
sigma_H[7] 0.300 0.059 0.206 0.291 0.435
sigma_H[8] 0.416 0.089 0.275 0.407 0.614
sigma_H[9] 0.527 0.127 0.331 0.512 0.822
sigma_H[10] 0.218 0.043 0.143 0.214 0.311
sigma_H[11] 0.278 0.046 0.202 0.273 0.379
sigma_H[12] 0.438 0.167 0.205 0.410 0.780
sigma_H[13] 0.213 0.036 0.152 0.211 0.292
sigma_H[14] 0.508 0.093 0.348 0.500 0.713
sigma_H[15] 0.246 0.040 0.178 0.243 0.332
sigma_H[16] 0.224 0.044 0.153 0.220 0.321
lambda_H[1] 3.111 4.051 0.152 1.801 14.408
lambda_H[2] 8.277 7.801 0.782 5.945 28.594
lambda_H[3] 6.155 9.278 0.257 3.072 30.024
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 4.255 9.933 0.033 1.026 30.994
lambda_H[6] 7.099 15.290 0.007 0.703 44.564
lambda_H[7] 0.014 0.010 0.002 0.011 0.040
lambda_H[8] 8.121 9.968 0.069 4.566 35.710
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.337 0.815 0.030 0.204 1.105
lambda_H[11] 0.277 0.432 0.012 0.136 1.272
lambda_H[12] 4.773 6.119 0.213 2.654 21.868
lambda_H[13] 3.511 3.215 0.236 2.575 11.950
lambda_H[14] 3.192 3.863 0.217 1.993 13.420
lambda_H[15] 0.026 0.039 0.004 0.017 0.108
lambda_H[16] 0.809 1.314 0.040 0.400 3.861
mu_lambda_H[1] 4.343 1.889 1.264 4.158 8.451
mu_lambda_H[2] 3.842 1.955 0.638 3.712 7.989
mu_lambda_H[3] 3.466 1.853 0.748 3.167 7.811
sigma_lambda_H[1] 8.643 4.277 2.202 8.004 18.196
sigma_lambda_H[2] 8.411 4.707 1.070 7.813 18.310
sigma_lambda_H[3] 6.227 4.053 0.958 5.362 16.590
beta_H[1,1] 6.883 1.099 4.288 7.036 8.540
beta_H[2,1] 9.865 0.498 8.779 9.899 10.778
beta_H[3,1] 7.977 0.812 5.995 8.061 9.302
beta_H[4,1] 9.560 7.605 -6.116 9.711 24.303
beta_H[5,1] 0.113 2.336 -5.070 0.258 4.103
beta_H[6,1] 3.131 3.991 -6.451 4.552 7.818
beta_H[7,1] 0.613 5.583 -11.255 0.959 10.504
beta_H[8,1] 1.410 4.220 -2.497 1.207 3.689
beta_H[9,1] 12.880 5.619 1.637 12.878 23.868
beta_H[10,1] 7.102 1.692 3.627 7.160 10.299
beta_H[11,1] 5.145 3.509 -2.931 5.890 9.977
beta_H[12,1] 2.630 1.040 0.826 2.553 4.958
beta_H[13,1] 9.036 1.022 6.891 9.137 10.525
beta_H[14,1] 2.198 1.048 0.155 2.206 4.247
beta_H[15,1] -6.009 3.806 -12.758 -6.295 2.371
beta_H[16,1] 3.556 2.663 -0.862 3.286 9.904
beta_H[1,2] 7.898 0.248 7.394 7.903 8.372
beta_H[2,2] 10.028 0.139 9.755 10.027 10.295
beta_H[3,2] 8.955 0.204 8.547 8.953 9.358
beta_H[4,2] 3.506 1.434 0.759 3.493 6.407
beta_H[5,2] 1.927 0.933 0.046 1.957 3.713
beta_H[6,2] 5.700 1.089 3.101 5.890 7.339
beta_H[7,2] 2.601 1.077 0.646 2.544 4.824
beta_H[8,2] 2.973 1.165 1.183 3.127 4.245
beta_H[9,2] 3.532 1.097 1.441 3.512 5.803
beta_H[10,2] 8.192 0.348 7.453 8.200 8.849
beta_H[11,2] 9.756 0.637 8.840 9.631 11.194
beta_H[12,2] 3.947 0.366 3.266 3.931 4.690
beta_H[13,2] 9.131 0.266 8.673 9.118 9.651
beta_H[14,2] 4.027 0.352 3.368 4.021 4.737
beta_H[15,2] 11.349 0.696 9.843 11.393 12.609
beta_H[16,2] 4.543 0.813 2.993 4.533 6.155
beta_H[1,3] 8.472 0.237 8.045 8.464 8.945
beta_H[2,3] 10.062 0.117 9.821 10.062 10.294
beta_H[3,3] 9.619 0.163 9.315 9.609 9.961
beta_H[4,3] -2.466 0.875 -4.212 -2.449 -0.801
beta_H[5,3] 3.826 0.603 2.629 3.838 4.991
beta_H[6,3] 8.046 1.204 6.353 7.680 10.597
beta_H[7,3] -2.688 0.690 -3.991 -2.690 -1.243
beta_H[8,3] 5.260 0.528 4.649 5.193 6.330
beta_H[9,3] -2.872 0.745 -4.402 -2.849 -1.433
beta_H[10,3] 8.704 0.273 8.179 8.700 9.240
beta_H[11,3] 8.550 0.289 7.904 8.576 9.058
beta_H[12,3] 5.260 0.314 4.503 5.305 5.758
beta_H[13,3] 8.837 0.177 8.495 8.839 9.179
beta_H[14,3] 5.715 0.283 5.094 5.736 6.218
beta_H[15,3] 10.366 0.313 9.789 10.353 11.000
beta_H[16,3] 6.203 0.624 4.858 6.268 7.220
beta_H[1,4] 8.266 0.182 7.872 8.279 8.588
beta_H[2,4] 10.129 0.123 9.864 10.142 10.349
beta_H[3,4] 10.116 0.163 9.758 10.130 10.409
beta_H[4,4] 11.790 0.446 10.877 11.798 12.637
beta_H[5,4] 5.482 0.755 4.296 5.393 7.230
beta_H[6,4] 7.040 0.935 4.939 7.301 8.309
beta_H[7,4] 8.196 0.346 7.488 8.203 8.833
beta_H[8,4] 6.707 0.267 6.199 6.722 7.140
beta_H[9,4] 7.219 0.461 6.303 7.206 8.160
beta_H[10,4] 7.763 0.241 7.291 7.760 8.256
beta_H[11,4] 9.385 0.202 8.985 9.384 9.786
beta_H[12,4] 7.145 0.209 6.743 7.137 7.595
beta_H[13,4] 9.044 0.141 8.762 9.041 9.320
beta_H[14,4] 7.741 0.219 7.305 7.741 8.182
beta_H[15,4] 9.473 0.237 9.018 9.469 9.932
beta_H[16,4] 9.358 0.245 8.922 9.347 9.868
beta_H[1,5] 8.982 0.142 8.698 8.986 9.251
beta_H[2,5] 10.782 0.094 10.597 10.783 10.976
beta_H[3,5] 10.927 0.175 10.611 10.919 11.273
beta_H[4,5] 8.394 0.469 7.479 8.377 9.354
beta_H[5,5] 5.391 0.579 4.020 5.450 6.353
beta_H[6,5] 8.844 0.637 7.946 8.700 10.342
beta_H[7,5] 6.811 0.334 6.164 6.813 7.484
beta_H[8,5] 8.218 0.228 7.854 8.199 8.672
beta_H[9,5] 8.212 0.468 7.278 8.228 9.113
beta_H[10,5] 10.079 0.238 9.598 10.086 10.535
beta_H[11,5] 11.508 0.226 11.061 11.508 11.950
beta_H[12,5] 8.484 0.196 8.099 8.485 8.883
beta_H[13,5] 10.011 0.131 9.757 10.007 10.275
beta_H[14,5] 9.210 0.237 8.764 9.202 9.703
beta_H[15,5] 11.163 0.245 10.684 11.166 11.638
beta_H[16,5] 9.911 0.180 9.539 9.919 10.248
beta_H[1,6] 10.176 0.195 9.842 10.161 10.605
beta_H[2,6] 11.515 0.108 11.296 11.515 11.723
beta_H[3,6] 10.800 0.165 10.441 10.813 11.088
beta_H[4,6] 12.879 0.825 11.250 12.894 14.456
beta_H[5,6] 5.908 0.612 4.749 5.901 7.139
beta_H[6,6] 8.760 0.686 6.929 8.903 9.720
beta_H[7,6] 9.803 0.554 8.664 9.801 10.925
beta_H[8,6] 9.516 0.292 8.981 9.537 9.959
beta_H[9,6] 8.470 0.792 6.939 8.439 10.164
beta_H[10,6] 9.514 0.322 8.812 9.540 10.087
beta_H[11,6] 10.817 0.345 10.092 10.855 11.414
beta_H[12,6] 9.370 0.252 8.884 9.363 9.905
beta_H[13,6] 11.044 0.163 10.745 11.035 11.388
beta_H[14,6] 9.825 0.292 9.244 9.823 10.384
beta_H[15,6] 10.839 0.434 10.001 10.845 11.688
beta_H[16,6] 10.544 0.242 10.028 10.549 11.010
beta_H[1,7] 10.864 0.872 8.723 10.970 12.277
beta_H[2,7] 12.223 0.437 11.346 12.233 13.041
beta_H[3,7] 10.541 0.676 9.106 10.597 11.669
beta_H[4,7] 2.474 4.204 -5.903 2.373 10.866
beta_H[5,7] 6.488 1.838 3.248 6.385 10.431
beta_H[6,7] 9.659 2.513 4.951 9.540 16.390
beta_H[7,7] 10.789 2.769 5.280 10.807 16.468
beta_H[8,7] 11.003 1.087 9.458 10.932 12.962
beta_H[9,7] 4.457 4.038 -4.104 4.551 12.197
beta_H[10,7] 9.797 1.479 7.054 9.693 12.999
beta_H[11,7] 10.941 1.684 7.821 10.815 14.557
beta_H[12,7] 10.012 0.914 8.042 10.104 11.536
beta_H[13,7] 11.663 0.751 9.966 11.758 12.821
beta_H[14,7] 10.378 0.964 8.333 10.405 12.169
beta_H[15,7] 12.059 2.261 7.679 12.062 16.496
beta_H[16,7] 12.290 1.279 10.164 12.143 15.268
beta0_H[1] 8.454 13.485 -19.194 8.702 35.509
beta0_H[2] 10.608 6.507 -3.072 10.629 23.560
beta0_H[3] 9.731 10.341 -11.525 9.945 29.413
beta0_H[4] 3.074 182.074 -373.029 10.411 370.331
beta0_H[5] 4.807 25.365 -39.555 4.520 50.473
beta0_H[6] 8.601 51.394 -96.975 7.666 116.131
beta0_H[7] 9.422 133.055 -251.089 7.097 276.028
beta0_H[8] 7.196 33.877 -16.917 6.452 29.817
beta0_H[9] 8.905 123.684 -237.472 8.429 252.585
beta0_H[10] 8.730 32.034 -58.311 9.031 72.591
beta0_H[11] 10.468 48.407 -93.678 9.909 120.723
beta0_H[12] 7.040 11.258 -15.501 6.937 28.534
beta0_H[13] 9.930 11.828 -11.691 9.763 30.704
beta0_H[14] 6.638 12.939 -19.281 7.057 29.506
beta0_H[15] 9.709 103.004 -207.472 11.764 215.355
beta0_H[16] 7.857 26.080 -46.562 8.197 60.415